The Labor Party will push the government to pass a same-sex marriage bill penned by Liberal senator Dean Smith if Australia votes "yes" in the postal survey.

The decision comes in the final few weeks of voting in the nationwide survey, which has yielded a turnout of over 60% despite being non-compulsory.

If a "yes" vote is announced on November 15, Malcolm Turnbull's government has promised to allow a conscience vote on a private members' bill for same-sex marriage.

It is expected the conscience vote would pass the parliament. But many are anticipating a parliamentary brawl over what the bill will look like.

In its caucus meeting on Tuesday morning Labor resolved to push the government to pass the Smith bill in its current form as quickly as possible.

The bill would continue the current exemption for religious ministers to refuse to marry a couple; provide a window for current civil celebrants to be afforded the same exemption; and allow religious organisations to deny goods and services to a same-sex couple wanting to wed, such as refusing to hire out a church hall.

It is based on a Senate inquiry into a same-sex marriage draft bill which delivered a report in February this year.

Labor resolved the bill is consistent with the recommendations in the bipartisan report, and that it strikes an acceptable compromise between legalising same-sex marriage and protecting religious freedom.

Neither the Greens nor the Nick Xenophon Team have an official position on their preferred bill in the event of a "yes" vote, while the government has repeatedly said the form of the bill is a matter for the parliament.

The "yes" campaign has loosely, though not unanimously, supported the Smith bill, while the "no" campaign has labelled it inadequate, but not offered concrete suggestions on how it might be improved.

In submissions to the Senate inquiry earlier this year, groups formally associated with the "no" campaign called for commercial business owners to be exempt from serving same-sex weddings on the basis of either religious belief or conscience.

Other submissions suggested the inclusion of a non-detriment clause that would offer a legal protection to anyone who speaks out against, or personally refuses to accept, same-sex marriage.

"I think the fact the Labor Party have endorsed a Liberal member's bill is a wonderful symbol of how marriage equality transcends party politics," he said.

As the government and Labor Party will have a conscience vote, predictions on how the Smith bill and any amendments might fare in the House and Senate are not clear cut.

The Smith bill was presented to the party room not just by Smith, but with the names of four lower house MPs on it: Tim Wilson, Trent Zimmerman, Trevor Evans, and Warren Entsch.

Meanwhile, there are a small number of Labor politicians in both houses who remain opposed to changing the Marriage Act and will likely vote against the bill. Labor's agreement to hold a conscience vote on the issue expires at the next federal election.

Tuesday's meeting was the last full caucus prior to the postal survey result being announced on November 15.

Lane Sainty is a reporter for BuzzFeed News and is based in Sydney, Australia.